# Free Will Theorem (Strong) - Conway & Kochen

I have not seen this discussed much.

The Free Will Theorem (FWT) does not prove that we have Free Will, or that things are Deterministic. Most people hear that -- so they often look for more interesting game elsewhere.

The theorem's usefulness lies in the corollaries that affect the philosophy of matter, mind and how they may interact. Also, it has an impact on the Determinist when asked how much determinism do you really have... one must have nearly a 100% deterministic world view.

Another concept (implied, if thought out) is that to get free will... one must use Quantum Computers/Mechanisms. Totally deterministic "anything" should not work. Penrose agrees in his book "The Emperor's New Mind". Quantum Computer technology is already a Consumer Of The Shelf (COTS) product. You had better be ready for it. (I may give the minimal "basics" if someone wants it - i.e. a serious person wanting it)

The Free Will Theorem states that if two experimenters are free to make choices about what measurements to take, then the results of the measurements cannot be determined by anything previous to the experiments. Since the theorem applies to any arbitrary physical theory consistent with the axioms, it would not even be possible to place the information into the universe's past in an ad hoc way.

The theorem assumes 3 axioms:

1)    Fin  (Finite): There is a maximum speed for propagation of the information (not necessarily the speed of light). This assumption rests upon causality.
2)    Spin: The squared spin component of certain elementary particles of spin one, taken in three orthogonal directions, will be a permutation of (1,1,0).  (Operationally definable)
3)    Twin: It is possible to "entangle" two elementary particles, and separate them by a significant distance, so that they have the same squared spin results if measured in parallel directions. This is a consequence of (but more limited than) quantum entanglement. (Operationally definable)

(The experimenter must have free will also)

Dr. Conway gave 6 Lectures (at Harvard Univ.) that are targeted for any freshman in Philosophy, Math or Physics. In general, they are a bit harder than he intended.

However, the "Heart" of all 6 are in the first and the last two (fifth & sixth). They are understandable for very many people. Dr. Conway gives good lectures, and he is very entertaining. He is a very famous Mathematician and rather acts like one. I highly recommend those three lectures.

The 6 Lectures (~< 1 hour each)

Above is recommended to view

The 3 lectures above are not for most people. However - the math is not that bad. I know several people on this site who would not have any problems. Also - to just watch the above, ignore the math details, and they are worth watching.

Above is recommended to view

Source Papers: (not very accessible to most)

The FWT paper:  Free Will Theorem (Arxiv.org)

I have also added Dr. David Mermin's 2-page paper (from Archive.org) that strengthens/assures that stochastic arguments fail (period).  Cloning a single Bit

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### Replies to This Discussion

It occurred to me that this is a pretty low-priority topic for most. However - if you do anything - I would recommend that you at least watch the first lecture. It is pretty good (and Conway is rather a humorous person)

John

Thanks John for this wonderful information. These are excellent videos. Even the maths is not so complex and is easily skipped.

Professor Conway establishes FWT by proving that the past history of the universe does not affect the choice of the particle regarding its spin. Can absence of determinism (a prediction based on the past history of the universe) prove existence of Free Will conclusively? Where does randomness fit in all this? For example, if the particles were following randomness (non-predictability), which would also be a law, how it can lead to Free Will?

Maybe he explained it too, but I could not understand it.

Somehow I was constantly reminded of Anekantvada of Jain Philosophy, throughout the lecture. Why am I wrong?

Hi Anand!

I glad you found these interesting!

"Can absence of determinism (a prediction based on the past history of the universe) prove existence of Free Will conclusively?"

The argument for Free Will versus Determinism can never be settled. The points in his first lecture regarding Determinism are very good in that a motion picture that violates all of physics can still be argued by a "determined Determinist" as a second showing of the motion picture, or first for that matter. It may just all be totally scripted for all time. No reasons need ever to exist. Hence - Determinism vs Free Will is not provable (ever). However, he has shown that the Universe contains situations that are not not predetermined in any way via physical laws. This is the key point of the theorem. That scenario is a very real one.

(but could be a part of the movie picture and hence determined)

The concept of randomness is subtle.

1) Probabilistic arguments do not work since the particles have no predetermined nature/probability of any sort. The subtle issue is that if it is totally random, then it would be like throwing a 6-sided die that has a 1/6 chance for any number. Also if the die is "weighted" the probabilities shift, but they still have a predetermined probability. QM is full of this.

The key difference is there is not even a probability that exists. It is like asking a person to pick one of 6 numbers. The person can choose anything he/she wants.  The person may decide to only/always pick the number 1, or the number 6, or only even numbers, numbers always less than 4,,,  anything can be given and no probability can ever be assigned. That is the subtle part between random and free choice. The particles have free choice and no probabilities.

Also another point is that it takes the experimenter's Free Will to force the issue home. That is a fascinating piece of the puzzle. Free Will is needed to get/give more Free Will. QM is also critical to create this phenomena. Hence QM computers are needed to get Artificial Intelligence. Classical computers and networks are just complex calculators. Penrose makes this point very well In his book "The Emperor's  New Mind".

Thanks for mentioning " Anekantvada". Looks like an idea that may fit my current thinking on the matter.

After looking at  Anekantvada, it struck me that this is very similar to the optional item 5 in the definition of Esotericism (FAQ). i.e. it is an option. Just  a side note; I have not studied it (Anekantvada) enough to make that claim....  I toss it out for a possible future discussion by someone who is knowledgeable in this. (??)

Also, how can one know the past history of the particle to say that its choice is not affected by its history. I believe the answer is given but again I could not understand it.

This is a very good question! It is again is a bit subtle. The Kochen-Specter theorem creates the conundrum which denies ANY predetermined solution/geometry, i.e. historically predetermined configuration/answer.Why??

That mess of cubes (built very cleverly) does NOT have a predetermined solution. It is impossible to preassign the reality in any way shape or form. The set of corners of the cube(s) create a mathematical, via geometry,  conundrum. Each corner is a possible orientation for the experimenter(s) to choose independently. NOTE: the corners actually are directions at the same point of measurement, only the directions are decided by the Experimenter. They are not measured at the different positions in space (corners of cubes) for the experimental equipment. The diagram (corners) of the different orientations are always at the single point of measurement. Gads, I hope I said that in an understandable way.

example of a simple mathematical conundrum:

(this is a fictional problem - just an example)

use two experimenters on two (QM configured) particles where one has to be a "0" and the other has to be a "1".  (never two zeros or two 1's). The measurement can be only done in one of 3 directions, each oriented differently adjacent to one of the three directions.

Look at the triangle of the three possibilities. Each vertex MUST be the opposite direction of the vertices next to it. All three corners must agree on this configuration. Now try to label the three corners. It is impossible. (A Conundrum). It is impossible to know any of the answers ahead of time, nor find a configuration that can ever be assigned. However, one Experimenter will get a 1 (or 0)  the other Experimenter can pick either of the remaining two vertices and he will always get a 0 (or one).

I hope you see the problem... the answers cannot be preassigned, even using probabilities. If the two Experimenters are a light-year apart....  how do the two particles (both) guarantee the (1,0) or (0,1) relations... ??

They are impossible to preassign.

Help any??

I am glad you saw the ones with the math.. the words are all that really matter. The three hypotheses are experimentally objective. go in any lab in the universe and each is true.

Dear John ,

I have been closely following this discussion , now what points I am not clear on are the following :

Is this thory talking about the Free Will as in a purely Metaphysical Manner and then trying to predict possible outcomes ?

Or is Free will alternatively not quite the Free will as in Metaphysics and rather another definition of Free Will that has been supposed so that it may lend itself to mathematical analysis or Scientific Analysis . Because I do detect some anomalies since , if it is the outcome of actions that are not predetermined are being sought to be assessed or whether it is the outcome of a predetermined action that is being sought to be forecast . Of course to use the Scientific terms and as NOT relating to a persons actions per se but rather to the outcomes of the behaviour of quantum particles due to a Stoachistic or a Deterministic modelleing whereby gaps in the different sciences or theories can be ascertained which would give an indication of the absence or prescence of the possibility of a particular axiom at that level which would bridge a cut or leap between sections of the same underlying theory . Now in Metaphysics we have the point of occultism whereby the thought process is reversed from the bottom up view to its opposite by employing the Top bottom View in order to bridge it . And in many cases the point of occultism at the Space time limit requires a metaphysical anlysis from the top to provide the bridge as everything else is exhausted at this limit . The conception of objects is no longer valid , but lower down the Breaks will provide insight into cross theories and other things which may help or not help mankind - but it is manifest knowledge and so Modelling is possible .

Is the future being sought to be forecast - devoid of causation or within causation is my question .

If such is the case is it not the case that knowledge is being sought - either a particular type or an axiomatic one .

Then the question comes as to whether a standard axiom at the quantum level is what is being looked for at a certain break (which would make it universally applicable at that particular level) - or is it an axiom or theorem applicable at that particular level to that particular obtaining situation , which obviously will be different and unquantifiable for another set of hypothesis or situation . Now is it again an observed knowledge that is being sought or whether a different kind of knowledge which may include the Observer also , but in the latter case quantification as a particular axiom will only follow if there are further grounds of existence obtaining to limit the observer - In short the theory would be in a Scientific manner not lend to analysis as each observer is conscious and the observed quantum result would be individual specific . Again is it that if we take say : Newtonian Physics and its rules and work our way down to the Quantum level and at quantum speeds etc etc is the scientific community trying to ascertain as in the Macrocosm whether there would be axioms pertaining to the QM in a like manner but in the microcosm - If this is the thrust of the idea in which Deterministic will or Stoachastic will is assumed is it not a travesty that there is an inquiry based on a preconcieved idea of the Macro system ?. Now if Philosophical Assumptions have to be made by a scientist it would not be valid unless he

a) Assumes certain notions of Free Will by his own understanding which would be at variance with the True Philosophical Axioms relating to Free Will .

B) On the other hand if the Scientist Takes the Philosophical Axioms as they are - then it will not lend itself to scientific manipulation and analysis as Metalogic is the logic of Philosophy . And more gaps than certainities will be there .

I am looking at this not from a philosophical angle , but trying to understand how this idea is evolving in the world and from where do they get these ideas - my reasons and interest are entirely different .

Now MIN is a pretty nebulous thing as far as science is concerned - it is more of an apology or an after thought by the originators when they resort to the third method . It happens commonly in scientific and in many reasoning areas by even common people where just to hedge against a collapse a third synthesis is mooted - which itself is a kind of bridge in a manner of speaking .

Another problem which I am facing in this discussion and from what I have read on the subject is that - Of all the millions of dimensions - Time unfortunately is only one dimensional , but runs through the whole arena , and there is another strange thing Will is unconcerned with time , but actions whether volitional or involuntary , meditated or premeditated are subject to time and so the result of such an employment of knowledge is time bound . Ie , The results ascertained would be variable and would vanish if a dynamic model is assumed and in the case of a deterministic model the results would still be variable in that all it would show would be where the result will occur within two determined limits - either outside or inside but never exactly - unless in order to get an exact point a suitably variable assumption of universal proportions is taken .

Or finally is this thing aiming at a specific end - by which I mean an end that is stated as either a Scientific Ideal or a Philosophical Idea ? - Because in the absence of a clear cut statement on the ideal there will not be any proper measurable results and so concomittantly the grounds for existence for such a foray will not be there . Here I use the words 'Ground for Existence'' of this branch of thought both in the philosophical and Scientific sense and so it covers the physical world and its practical applications for humankind.

Once again why I am asking all these queries is because is by the word Free Will the scientific community meaning "anything that generates knowledge '' or is the word used in the sense as applicable to the Conscious and Finite Observer who then is obviously and agent and so has instruments , and if the instruments assumed by Ms.Conway and team are a conscious instrument or an instrument which is non conscious - because these again will give significantly altered states of knowledge for the same experiment .To clarify One would be like 'studying and gaining knowledge on death'' by observation of the phenomena in others and the other would be "the actual undergoing of the phenomena by a person ".

In an embodied Agent will is free , choices are there , determinations are individual etc etc (This is not the actual situation - but it is the actual way we behave in the world ). Now why would the instrument be added as a parameter in an observation - I can understand that in case of some physical quanta corrections would be required to eliminate the "white noise''.  But elimination of the observer per se ......it does not make sense - for in a way one has to assume two things

a)either the observation will be invalid on an apriori assumption - and therefore the outcome is totally bereft of the initial willing of observation .And whatever the out come . it has to be assumed to be as falling within "The grounds for existence"

in which case a "working back from results may suffice to first state the grounds of Existence - which would be more palatable .

b) Embodied  Willing being bereft of time results in knowledge that is "subject'' to time and so the result has to be equated to the Ideal and how far or close it may be .

In both the above manners a modicum of decency in argument and structure can be discerned.

Why I write this is because in relation to the human beings will (the so called free will) we have as a standard in Philosophy the ability of Intuition .

Intuition is bereft of Time and yet for an embodies person it is experiential - Intuition transcends reason but does not controvert it . Let me try to explain with an example :

In Intuition the RESULT is assured - the methodology is not known at the time of making the Willing of an action , and the action if analysed will not lend itself to causation - but over time and a succession of events the action done involuntarily is

ratified by the result obtained - wherein if the person next does a posterior analysis of the action would find that it was the perferctly knowledgeable and reasonable course to have indulged in - though unknown to himself at the time of acting - in this case Willing is the same as Action - the action done would only be a perfunctory movement of the instrument without doership........ This gain would in a way complicate the case of the "conscious'' instrument .

To what end is all this required is my question and does the end embrace a lot of people or just a few or just one ?

Dear John ,

Again as a postscript what I would like to enumerate is something - in Science is the evidence of a result or the spotting of a result necessarily the result of a proof ?. Or is something proved by positive evidences or its corollary the negative ones ?. because rarely does a thing stand up to scrutiny if it is totally proved by negative evidences , there is only one such thing so far known to mankind where the knowledge gained completely of a thing is by negative evidences and that is the Experience of the Pure Self reflected in the Intellect . It is a reflective knowledge . But here again what is pertinent to note is that - the negative evidences are in fact positive when the Ideal is the realization of the self which is a non object . On the other hand in the matter of the manifest world an evidence or proof consists of both positive and negative proofs , since the objects of knowledge are reflective in nature with regard to a non object but within themselves they are providers of positive evidences . Of course in matters related to concepts "beyond space'' but before the Self there is fluidity - it is always a mixed nature of action particularly if a person has a habit of working out of his mind , and if from the intellect then negatives will prove the concept in most cases as it deals with ignorance and knowledge . Really speaking Ignorance is partial knowledge so it deviates from existence .  There are not that many things which will lend itself to scrutiny with an "open and active phyisical eye" which are suitably Quantum in nature . Sound,Light and Energy can be split up at a certain level of knowledge from the images in the mind and they result in Quantum Knowledge of these entities. but it is inner and will not lend to an examination by an observer which is in the consciousness of the body . The nearest that can be done however is the monitoring of the brain - but this would only be a Physical interpretation of the phenomena and incomplete since the material composition of the brain and its manifestations of power are significantly smaller than the mind or the intellect . SCientifically many possibilities are there to dabble in the more remote corners of physics but again - The Physicological extensions of the human Psyche into the Psychological areas were initially huge when Freud,Addler and Jung started out - then again by a circutous route the sciences again turned back into the psycho logical arena when the brain came in for examination - In a way it was a retrograde step . experiments into the brain have its limited uses in medicine only , it may to an extent help in getting some dead parts to work in a manner where a blind man may  see or a deaf hear - would it not be easier for them to sit down and meditate and actually see the world as we see but  without any help of the physical eyes ? . THe mind and intellect can see the world more clearly as we see - devoid of the organs and to scale not small or big but as is normally seen by a proper human being . What is it that is stopping the Scientists from examining this possibility which many people are actually doing in their life time ?

Hi Hari!

Conway is very explicit on the limitations of the theorem. He limits the amount of free will by the experimenters to a rather miniscule choice between some buttons to press and the event (shared on each side) has 1 bit of freedom between both of the events. The causal constraints are everywhere, as a full-fledged Determinist could want. Yet that tiny bit of choice shared between the Experimental Events is decided freely without the capability to force fudge factors to explain things away in a causal loop-hole of Randomness/Probabilities/Chaos/Hidden-Variables/Super-luminal-communication or anything normally used to justify a fully determined Universe. So, this isn't about Free Will (purposefully left undefined) and consciousness as much as it eliminates fuzzy notions on where and what ground the Determinist has left to stand on. You have to be pretty much a "Determined Determinist".

David -

The theorem does not try to prove that you have Free Will. That is impossible, as well as is proving Determinism wrong.

It seems Hari Menon is not the only one disagreeing with the axiom of MIN. There is another Menon, Tarun Menon who does so. His paper is attached. Why are all the Menons so clever? :-)

Attachments:

Hi !

Mermin's paper eliminates Min. It also derives the result directly, by using only QM. That is why he has the claim that it strengthens the theorem.  Mermin's paper is rather unreadable by nearly everyone not familiar with QM. The FWT has a easier conceptual argument, which can be used for other paradoxes, not just Kochen-Specter. The other item is that Kochen-Specter has the impossibility of any hidden-variables which allow a predefined state in the particles.

To get rid of Min, you have to throw out all of General Relativity. Not a likely scenario.

I should add that making the set of options for the experimenters' free will as small as possible is purposefully constructed to make the theorem stronger, not weaker. It constricts the free-will action so Determinism has less to work with w.r.t. denying free will. If one could make the free-will capabilities of the experimenters even smaller, then that would make for a stronger theorem.

GRW uses instantaneous collapse as a valid solution to QM paradoxes. It is inherently a Deterministic assumption from the start.

John